Just finished this excellent book by Jim Albert and Jay Bennet originally published in 2001 but updated after the 2002 season. This book starts out with a discussion of models that tabletop baseball games such as Cadaco All Star Baseball, APBA, and Strat-o-Matic use. The authors then go on to discuss statistical models and how they apply to baseball. I'll summarize some of their interesting (although not all of them definitive) conclusions:

Outs/Bases | 0 | 1 | 2 | 3 | 1,2 | 1,3 | 2,3 | 1,2,3 |

0 | .511 | .896 | 1.142 | 1.405 | 1.511 | 1.838 | 1.956 | 2.332 |

1 | .272 | .536 | 0.682 | 0.944 | 0.936 | 1.185 | 1.358 | 1.510 |

2 | .101 | .227 | 0.322 | 0.363 | 0.450 | 0.524 | 0.633 | 0.776 |

They then include a probabality of scoring table from Lindsey's 1959 and 1960 data (I can't seem to find a more recent version of a table like this although the authors showed that Lindsey's data in general was fairly close to more recent compilation although Lindsey's sample size is not that large since there were only 16 teams during that era):

Outs/Bases | 0 | 1 | 2 | 3 | 1,2 | 1,3 | 2,3 | 1,2,3 |

0 | .253 | .396 | 0.619 | 0.880 | 0.605 | 0.870 | 0.820 | 0.820 |

1 | .145 | .266 | 0.390 | 0.693 | 0.429 | 0.633 | 0.730 | 0.697 |

2 | .067 | .114 | 0.212 | 0.262 | 0.209 | 0.283 | 0.332 | 0.329 |

With this data it is relatively easy to evaluate when to steal bases, when to bunt, and when to intentionally walk a batter. In short they find that stealing 2nd base is advantageous as long as the runner has a probability of success of greater than 60%. Of course, the probability threshold goes down (into to the low 50s) in the later innings when the team is simply trying to score 1 run. This is interesting since most common wisdom I've always heard says that the SB % needs to be around 67% to be effective.

For bunting the conclusion is that only weak hitters should bunt in the early innings (per MoneyBall and most other sabermetric research) and otherwise bunting should only be done in late innings when the objective is to score a single run.

For intentional walks they used Barry Bonds as the test case and calculated that walking Bonds only makes sense with a runner on 2nd and 2 outs or 1st and 2nd with 2 outs (using 2002 data). Other situations either definitely call for pitching to him or are too close to call statistically. (chapter 8)

In all, this is a great exploration of some of the core sabermetric concepts.

Incidentally, the tables and formulas provided by the authors vindicate my earlier rant about Dusty Baker bunting in the early innings of the NLCS. The situation was Lofton on 1st nobody out, Grudzlienack batting. If Grudz attempts to bunt the probability of scoring is 36.5% calculated as p of scoring = ((ps * pss) + (pf * pfs)) where ps is the probability of a successful sacrifice, pss is the probability of scoring with a runner on 2nd and 1 out, pf is the probability of the sacrifice failing and pfs is the probability of scoring with a runner on 1st and 2 outs. So (.8 * .390) + (.2 * .266) = .365. If Grudz does not bunt the probabilty of scoring is 40.4% (including calculating a double play). This calculation is performed simply by calculating Grudz odds of walking, hitting a single etc. and then multiplying that by the probability of scoring at least one run in the base-out situation that results and then adding the products.

Maybe not a huge difference but bunting also takes the Cubs out of the big inning moving the run potential from .896 to .682. A no-win situation. Of course in 2003 the three teams with the lowest number of sacrifices hits were the Blue Jays (11), A's (22), and Red Sox (24). All 3 of these teams have sabermetric minded GM's. Not suprisingly, the Cardinals led the NL with 87. I wonder if that will change with their new emphasis on sabermetrics per an earlier post.

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